/*
www-ATLAS of Group Representations.
2.S4(5) represented as permutations on 624 points.
*/

G<x,y>:=PermutationGroup<624|\[
2,4,6,8,10,9,13,1,15,14,18,19,16,22,3,25,26,23,24,30,31,5,34,35,7,
33,39,40,42,36,37,46,47,11,12,51,52,54,48,49,57,50,59,60,62,53,17,66,67,69,
20,21,73,65,75,76,68,78,70,71,82,72,84,85,87,27,28,90,29,92,93,95,32,98,88,
89,102,91,104,105,107,94,110,96,97,113,38,115,116,41,118,43,44,122,45,124,125,114,128,129,
131,117,134,119,120,138,121,140,112,123,143,145,126,147,55,56,151,58,153,154,156,61,158,63,64,
161,162,148,149,166,150,168,169,152,172,173,175,155,178,157,181,182,159,185,160,187,74,189,190,192,
77,195,79,80,199,81,201,83,203,109,86,188,207,208,210,191,213,193,194,217,218,196,197,222,198,
224,225,200,228,229,186,202,233,234,204,237,205,239,99,100,243,101,245,246,103,249,250,252,106,255,
108,258,111,261,262,263,240,241,267,242,269,270,244,273,274,276,247,248,280,281,283,251,286,253,254,
289,290,256,257,294,277,296,259,260,300,298,141,303,127,306,307,309,130,312,132,133,316,317,135,136,
321,137,323,324,139,327,328,142,331,332,144,146,305,336,337,339,308,272,310,311,344,345,313,314,340,
315,302,341,350,318,319,354,320,355,356,322,359,361,325,326,364,365,367,329,370,330,221,334,373,333,
376,377,335,206,304,163,164,383,165,384,385,167,388,389,391,170,171,394,395,297,174,399,176,177,351,
402,179,180,406,407,183,184,410,408,412,380,381,414,382,390,392,271,416,386,387,418,419,338,421,393,
226,423,425,396,397,398,430,431,400,433,401,435,436,403,404,439,405,427,437,378,442,422,409,445,446,
411,231,449,450,452,453,455,209,211,212,342,268,214,215,456,216,457,462,219,220,465,466,467,223,470,
472,227,475,476,478,230,232,236,483,235,486,238,488,454,490,458,492,459,460,349,461,482,463,496,464,
428,479,499,501,468,469,504,471,506,473,474,480,508,477,511,512,481,513,440,484,485,516,517,295,487,
514,264,265,348,266,275,278,497,522,523,420,279,525,527,282,284,285,531,532,287,534,288,536,537,291,
292,540,293,528,538,518,524,299,544,545,301,494,519,495,520,550,521,552,379,554,526,343,447,529,556,
530,557,558,533,560,535,500,539,413,551,541,542,543,548,569,546,547,371,509,570,571,346,347,372,352,
574,353,368,426,576,357,358,579,360,581,362,363,369,582,366,444,584,585,374,375,498,587,566,565,555,
583,572,515,573,590,575,577,578,591,580,593,594,596,597,564,451,598,503,586,415,417,601,489,424,507,
429,599,568,432,603,434,438,600,441,443,553,448,608,610,491,602,612,604,605,563,606,549,607,502,510,
493,617,505,619,615,595,620,611,621,616,614,618,609,588,562,623,559,624,561,567,622,613,589,592]
,\[
3,5,7,9,11,12,1,14,16,17,2,20,21,23,24,4,27,28,29,6,32,33,8,36,37,
38,10,41,43,44,45,13,48,49,50,15,53,55,39,56,18,58,19,61,63,64,65,22,68,70,
71,72,25,74,26,77,62,79,80,81,30,83,31,86,88,66,89,34,91,35,94,96,97,99,100,
101,40,103,42,106,108,109,57,111,112,46,114,47,117,95,119,120,121,51,123,52,126,127,54,130,
132,133,135,136,137,59,139,60,141,142,144,146,113,148,149,150,67,152,69,155,157,145,90,159,160,
73,163,164,165,75,167,76,170,171,78,174,176,177,179,180,82,183,184,84,186,85,188,87,191,193,
194,196,197,198,92,200,93,202,204,205,161,206,98,209,211,212,214,215,216,102,219,220,221,104,223,
105,226,227,107,230,231,232,110,235,236,122,238,240,241,242,115,244,116,247,248,118,251,253,254,256,
257,259,260,124,125,264,265,266,128,268,129,271,272,131,275,277,278,279,134,282,284,285,270,287,288,
138,291,292,293,140,295,297,298,299,143,301,302,304,305,147,308,310,311,313,314,315,151,318,319,320,
153,322,154,325,326,156,329,330,158,333,334,335,262,162,338,340,341,342,343,175,166,346,347,274,168,
348,169,349,351,352,353,172,258,173,357,358,360,362,317,363,178,366,368,369,181,371,182,372,374,375,
185,378,379,187,380,381,382,189,345,190,386,387,192,390,377,392,393,195,396,397,398,385,400,401,199,
403,404,405,201,283,408,409,203,411,263,413,367,207,339,208,415,210,417,309,344,213,370,420,217,422,
218,424,426,427,428,429,222,432,365,224,434,225,423,437,438,228,440,229,441,273,443,233,444,234,447,
448,246,237,451,239,454,456,457,458,252,243,459,460,389,245,414,461,289,463,464,249,250,468,469,471,
473,474,255,477,479,480,481,482,484,485,261,487,489,421,267,491,269,493,494,276,391,495,290,280,497,
281,498,500,502,430,503,286,505,507,508,509,501,359,510,337,294,419,296,514,445,515,300,490,388,518,
303,519,478,306,455,307,520,521,312,449,316,524,526,499,528,529,530,321,533,476,323,535,324,525,538,
539,327,541,328,542,543,331,511,332,546,547,548,549,336,376,527,551,553,442,350,496,555,354,395,355,
364,356,559,504,561,562,361,563,564,565,566,567,568,373,517,465,446,523,554,383,384,572,450,573,402,
394,416,516,575,577,531,578,399,580,556,582,488,576,470,583,453,406,407,544,586,410,570,412,537,588,
589,552,418,452,425,472,585,557,431,592,433,595,435,436,439,483,591,599,522,486,600,569,462,574,466,
475,467,602,579,604,605,606,597,607,558,587,545,609,492,611,512,613,593,614,506,581,540,615,513,616,
601,532,618,534,596,536,617,598,550,610,622,612,560,620,608,571,584,621,619,594,603,590,623,624]
>;
print "Group G is 2.S4(5) < Sym(624)";